Slice surface mesh with polygon
The reason why your polygon cut is larger than that of the original polygon is that you are performing the Knife Projection in perspective view. To make sure it maintains its scale, switch to orthographic view.

This can be explained as follows. If one want to Kinfe Project a circle onto a plane, the perspective projection of the circle is related to the field angle or focal length and the position of the camera as shown in the figure below. On the other hand, orthogonal projection is performed regardless of the position of the camera or any other property, also shown in the figure below. So, the scale of the perspective projection is directly proportional to the field angle while it is always constant in orthogonal projection.